Kelly betting is a strategy for gambling, maximizing one's log(money) every round, by betting a fixed fraction of one's income. I will define Kelly betting a certain class of discrete prediction markets, give a simple Kelly betting rule for these prediction markets, and show it equivalent to the original Kelly formula in a two-outcome case.

A prediction market consists of a finite set of outcomes O, and a probability measure Q(O) on these outcomes. Participants may buy, for some outcome o, a contract that pays out $1 if o comes true, for a price of $Q(o). This assumes no transaction fees.

Suppose you have m money. You are going to spend all your money on these contracts, with R being a probability measure over O, and R(o) being the portion of money you spend on each type of contract. Note that you [...]

---

First published:

Source:

Linkpost URL:
https://unstablerontology.substack.com/p/simple-kelley-betting-in-prediction

Narrated by TYPE III AUDIO.